2024 : 11 : 13
Asghar Rahimi

Asghar Rahimi

Academic rank: Professor
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Education: PhD.
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Research

Title
An Appropriate Representation Space for Controlled g-Frames
Type
JournalPaper
Keywords
Controlled g-frame · Controlled g-dual frame · Trace class operator
Year
2021
Journal Bulletin of the Iranian Mathematical Society
DOI
Researchers MARYAM FORUGHI ، ، Asghar Rahimi ، MOJGAN JAVAHERNIA

Abstract

In this paper, motivating the range of operators, we propose an appropriate representation space to introduce synthesis and analysis operators of controlled g-frames and discuss the properties of these operators. Especially, we show that the operator obtained by the composition of the synthesis and analysis operators of two controlled g-Bessel sequence is a trace class operator. Also, we define the canonical controlled g-dual and show that this dual gives rise to expand coefficients with the minimal norm. Finally, we extend some known equalities and inequalities for controlled g-frames.